Mr Gove said Charlie Whelan was a 'sour influence' on Labour
The Conservatives have stepped up attacks on Gordon Brown over his links with the political director of the union behind the BA strike.
They say Mr Brown should have given Charlie Whelan - his former spokesman - a "wide berth" yet claim he is "at the heart of Labour operations".
Shadow education secretary Michael Gove said Mr Whelan was "a sour influence".
Labour called it "a desperate attempt" to distract voters from the controversy surrounding Tory donor Lord Ashcroft.
Mr Whelan worked as Mr Brown's press secretary while he was chancellor, but resigned in 1999 over leaks surrounding Peter Mandelson's resignation over a home loan.
He is now political director of Unite, Labour's largest donor, which is behind the planned British Airways strike.
On Monday Mr Brown told the BBC the strike was "deplorable" and "unjustified", following similar comments from Transport Secretary Lord Adonis on Sunday.
But, ahead of a general election expected to be held on 6 May, the Conservatives have launched posters questioning the prime minister's links with Unite, with the slogan "Cash Gordon".
In a speech on Tuesday, Mr Gove attacked the influence of Unite - and Mr Whelan in particular - on Labour.
He said: "You would have thought prime ministers with a moral compass, who 'never engage in divisive and partisan politics' who stand on the steps of Downing Street promising to 'reach out beyond narrow party interest' would give figures like Charlie Whelan a particularly wide berth.
"Unfortunately not, because today, Mr Whelan is not just political director at Unite, he is working in Downing Street, masterminding Labour's election campaign."
Mr Gove claimed that "the dead hand of union pressure - and the sour influence of Charlie Whelan" had led to Mr Brown watering down plans for public sector reform.
'Knock heads together'
Shadow transport secretary Theresa Villiers raised the issue of BA in the Commons, asking whether Mr Brown had "spoken directly to Unite officials to urge them to call off the strike".
She also claimed Labour had accepted more than £300,000 from Unite on the same day that BA announced plans to strike over Christmas.
Transport Minister Sadiq Khan responded by accusing the Conservatives of "seeking to politicise what is an industrial dispute".
Liberal Democrat transport spokesman Norman Baker asked Mr Khan what steps he was taking to "knock heads together" and ensure the dispute was resolved.
Mr Khan said ministers had been in contact with both sides, but it was "unhelpful if we give a running commentary".
A Labour spokesman insisted ministers had been "unequivocal in their criticism of the strike plans by Unite" and that donations from union supporters "do not buy power".
"This is a painfully obvious and desperate attempt by the Tory party to turn the tables on party funding, but the reality is they are the party that has the questions to answer.
"The great elephant in the room of Lord Ashcroft is not going to go away by this unsubtle attempt to create a smokescreen."
Lord Ashcroft, the Tories' deputy chairman and biggest single donor, announced at the beginning of March that he was a "non dom" - someone who does not pay UK tax on overseas earnings.
As parties step up election campaigning, an ICM poll of 1,002 people for the Guardian found that 44% wanted the general election to result in a hung parliament, in which no party has an overall majority.
Almost a third of those questioned thought a clear Conservative win would be best for Britain, while 18% favoured a definitive Labour victory.